Question

The product of any three Consecutive number is always divisible by 6 give examples Why is this so

Answer 1

Let 1st consecutive number be x, then the next two consecutive numbers would be x+1 and x+2.

Let us put value of x as 1, so we will have numbers 1, 2 and 3.

We know that if a number is divisible by 2 and 3 both, then the number would be also divisible by 6.

And if we take 3 consecutive numbers, there must be 1 or 2 even numbers out of the 3 numbers.

And any number multiplied by an even number will give an even number as an outcome.

So the product of 3 consecutive numbers will be divisible by 2.

There must be 1 number out of any 3 consecutive numbers which would be divisible by 3.

eg- 102, 103, 104 are any 3 consecutive numbers and there must be 1 number out of them which would be divisible by 3... which is 102.

And any number multiplied by a multiple of 3 would give a product which would be divisible by 3.

So the product of 3 consecutive numbers will be divisible by 3.

And hence the product of any 3 consecutive numbers is always divisible by 6.

Hope it helps.